1. Field of the Invention
The present invention concerns a method to determine k-space positions for modeling radio-frequency (RF) pulses for magnetic resonance excitations, as well as a magnetic resonance apparatus and a computer-readable storage to implement the method.
2. Description of the Prior Art
One source of unwanted artifacts in magnetic resonance exposures (MR exposures) is spatial variations in the distribution of an applied radio-frequency field (RF field) in the examination volume (also called B1 or RF field inhomogeneities). These RF field inhomogeneities intensify as the strength of the basic magnetic field that is used is increased. Factors that lead to such RF field inhomogeneities are, for example, the local dielectric properties and the local conductivity properties in an examination subject that can shorten the RF wavelengths or, respectively, attenuate the RF amplitude. For example, spatially inhomogeneous RF fields generate locally different flip angles in the excitation and refocusing of the transverse magnetization of the nuclear spins. This leads to spatial variations of the MR signal strength and the image contrast (i.e. to unwanted, artificial shadowings in the MR image), particularly in whole-body imaging (breast, abdomen, pelvis), but also in head acquisitions (in particular at higher field strengths).
One method to regulate the spatial distribution of an excitation—in particular the excitation or, respectively, refocusing flip angle—is to directly affect the spatial distribution of the RF field via simultaneous transmission of RF pulses with multiple, spatially separated transmission coils. The respective phases and amplitudes are adjusted in the individual transmission channels so that the overlay of the individual fields corresponds to the desired RF distribution. This method is also called “RF shimming”. It is robust, independent of the flip angle to be achieved, efficient with regard to the specific absorption rate (SAR) and largely independent of the MR acquisition sequence that is used. However, the degree to homogeneity of the RF field that can be achieved with this method is limited. The achievable homogeneity in particular depends on the number of available parallel transmission channels. Providing independent transmission channels is expensive.
An additional method to affect the spatial distribution of excitation and refocusing flip angles is known as spatially selective excitation in the examination subject. A spatial modulation of the generated transverse magnetization is achieved by simultaneous action of RF and gradient pulses on the spin system in the examination subject. In principle, the spatial homogeneity of an RF excitation or refocusing that can be achieved in this manner is not limited, but the RF pulses that are required for this require disadvantageously long pulse times. However, the pulse times in the spatially selective excitation can in principle be shortened again by a parallel transmission with multiple transmission coils.
A known method for modeling RF pulses (in particular for a spatially selective excitation) is the original “spokes method” introduced by Saekho, which is described, for example, in Saekho et al.: “Fast-kz Three-Dimensional Tailored Radiofrequency Pulse for Reduced B1 Inhomogeneity”, Magnetic Resonance in Medicine 55:719-724 (2006).
The “spokes method” uses short gradient pulses (“spokes”) that are radiated between a few RF pulse segments. The k-space trajectory (associated with the gradient trajectory through the time integral) represents the path in k-space in which data are entered at individual points in k-space, but describes only a few k-space positions in the frequency space corresponding to the image plane. However, the ability with such a “spokes method” to an achieve homogeneity of the generated transverse magnetization can fluctuate significantly with a chosen number and selection of k-space positions of the spokes that are used. An applicable flip angle range and the SAR efficiency also depend on the selected k-space positions.
In different variants of the “spokes method” different approaches exist to choose the k-space positions that are used. In most cases—as in the article from Saekho that was already cited—the number and the coordinate of the k-space positions are simply provided by default.
Other variants attempt to optimize at least the positioning of the spokes. For example, Yip et al., “Advanced Three-Dimensional Tailored RF Pulse for Signal Recovery in T2*-Weighted Functional Magnetic Resonance Imaging”, Magnetic Resonance in Medicine 56:1050-1059 (2006) describes how a positioning of a predetermined number N of k-space positions to be used can be determined from the spectrum of the desired excitation pattern. The N k-space positions with the highest energies are thereby selected from the spectrum of the desired excitation pattern as k-space positions that are to be used. This method is limited, however, to only the transmission with one channel.
Other variants also attempt to optimize the number of spokes. For example, Zelinski et al.: “Fast Slice-Selective Radio-Frequency Excitation Pulses for Mitigation B1+Inhomogeneity in the Human Brain at 7 Tesla”, Magnetic Resonance in Medicine 59:1355-1364 (2008), describes how to reduce a number of spokes at discrete k-space positions to a low number by means of a complex mathematical method. Due to its high complexity, this method requires significant computing time. Moreover, it is not taken into account how robust an RF pulse optimized in this manner is against measurement errors in the calculation of detailed parameters (in particular those known as “B1 maps” that represent an achieved transversal magnetization) for the determination of a desired excitation pattern and against system imperfections. Moreover, the complex mathematical solutions are physically less transparent.